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Belt Loop and Shaft Frequency Calculator

Calculate ideal no-slip belt-loop frequency, pitch-line speed and shaft frequencies from matching pitch/datum dimensions.

Pitch/Datum GeometryNo-Slip KinematicsReference, Not Diagnosis

Model boundary: use pitch diameter and pitch length for synchronous belts, or a manufacturer-consistent datum/effective diameter and length for V-belts. Outside diameters are not interchangeable. Slip, elastic creep, tensioner motion and span resonance are not modelled.

Kinematic Results

Belt-loop frequency
Pitch-line speed
Driver shaft frequency
Driven shaft frequency / speed
Speed ratio n₂/n₁ = d₁/d₂

Mathematical loop-frequency harmonics

ВишеструкоHzcycles/min

Harmonic presence alone does not identify a unique fault or severity.

Ideal no-slip kinematics

v = π d₁ n₁ / 60,000   [m/s]
фпетља = v / (L/1000) = π d₁ n₁ / (60 L)
n₂ = n₁ d₁/d₂;   f₁=n₁/60;   f₂=n₂/60

All length inputs must describe the same pitch/datum system. Gates distinguishes pitch diameter from outside diameter for synchronous sprockets; Optibelt likewise distinguishes timing-belt pitch diameter and V-belt datum diameter/length.

Извори: Gates Light Power and Precision Manual, Gates timing-belt design manualи Optibelt V-belt manual.

Diagnostic boundary: a localized belt feature can repeat at loop frequency, but harmonics are not one-to-one fault labels. Belt-span natural frequency requires tension, free span, mass per length and boundary conditions; it is not bounded universally by the two shaft frequencies.

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General no-slip belt kinematics; not an ISO formula or automatic fault diagnosis. Scientific review: July 2026

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